The sister of a girl who died after suffering online abuse is struggling after being targeted by cyberbullies, it has been reported.

Hannah Smith, 14, from Lutterworth, Leicestershire, killed herself on Friday after being bullied on the website ask.fm, her father said.

Her sister Jo, 16, told the Daily Mirror she was now being subjected to the same hateful taunts her sister was as they prepared for her funeral.

"I've just lost my sister and now I've got to deal with getting abuse myself," she told the Mirror.

"These trolls don't care what happened to Hannah or what we're going through, they just live in their sad little worlds. It's really upsetting. I'm struggling to cope with what's happened and don't need these trolls hounding me."

Jo described her sister as "a beautiful person and so full of life and love". Smith said Hannah was found dead in her bedroom by her sister.

The website ask.fm has described Hannah's death as a "true tragedy" and promised to work with police investigating the incident.

The site allows users to send messages to one another without their identities being disclosed. Although users have to register an email address, name and date of birth, those posting messages can do so anonymously.

A spokeswoman for ask.fm said in a statement: "Hannah Smith's death is a true tragedy; we would like to convey our deepest condolences to her family and friends.

"We have reached out to the Leicestershire police and would be happy to co-operate with their investigation into the true circumstances of her suicide.

"Ask.fm actively encourages our users and their parents to report any incidences of bullying, either by using the in-site reporting button, or via our contact page. All reports are read by our team of moderators to ensure that genuine concerns are heard and acted upon immediately – and we always remove content reported to us that violates our terms of service."

Smith, 45, a lorry driver, called on David Cameron to put regulations in place on social networking websites to prevent another tragedy.

He wants the authorities to close ask.fm, and sites like it, after finding cruel taunts from trolls. He told the Leicester Mercury: "Websites like this are bullying websites because people can be anonymous. If I had not spoken up about this, another teenager could be dead next week.

"Ask.fm and sites like these are making millions out of people's misery and it is wrong. I would appeal to David Cameron as a prime minister and a father to look at this to make sure these sites are properly regulated so bullying of vulnerable people like my daughter cannot take place.

"I don't want other parents to go through what I am going through."

Smith described his devastation over his daughter's death. "We sleep downstairs now, we don't have a bedtime," he said. "Since this happened I have only had three hours' sleep a night.

"I want this to be sorted out as soon as possible so no other vulnerable children die."

He described his daughter as a "bubbly, happy person", adding: "She was colourful, she was a normal teenager and was very, very happy. For Hannah to do something like this … We never expected this. We never saw any signs of her doing this.

"I have now got to concentrate on burying my daughter. I need to be left alone to bury her and to grieve properly for her."

Nora Parker, headteacher at Lutterworth high school, said staff and students were deeply upset at the death of Hannah, who she said had just completed her final year at the school and was hoping to transfer to Lutterworth college this month. Hannah was a "bright, bubbly, popular and thoughtful girl who was liked and respected by all those she came into contact with. She had everything to live for and her family, who are utterly devastated, are at a loss to understand why this has happened."

More than 45,000 people have "liked" a Facebook tribute page. The page says: "Hannah Smith; a beautiful young girl who everyone loved very much; who decided to take her own life after being bullied; we will miss you princess; loveyou."

An online petition calls for greater measures to tackle websites such as ask.fm.

It states: "Cyberbullying has been an ever increasing problem within the UK for a considerable amount of time, with one of the biggest offenders becoming ask.fm, a site popular amongst young people where posts can be made with confidence anonymously which has led to bullying, mental health problems and suicides as well as grooming."

Organisations that tackle bullying called on internet service providers to work with government, police and schools to address online abuse.

Emma-Jane Cross, of BeatBullying, said: "We cannot stand by while innocent children lose their lives. Adults need to set an example for young people and we all have a responsibility to tackle this type of behaviour and keep our children safe.

"We want internet service providers, schools, government and the police to come together and produce a UK anti-bullying strategy, to prove that this kind of behaviour will not be tolerated."

Peter Wanless, chief executive of the NSPCC, said: "This is a tragic case where Hannah felt like she had no other option but to end her life. The cruel nature of cyberbullying allows perpetrators to remain anonymous and hide behind their screens.

"This is something that must be tackled before it gets out of hand. We must ensure young people have the confidence to speak out against this abuse, so that they don't feel isolated and without anywhere to turn."

Hannah's death comes amid growing concern about the policing of social media after rape and bomb threats were made to female media personalities on Twitter.

'If websites don't clean up their act ... then we as members of the general public have got to stop using these particular sites and boycott them,' the UK prime minister, David Cameron, has said. Do you agree with him?